Welcome to the Underdark! As you are now on the run, and actively travelling the mass of tunnels, chambers, and features that make up this wondrous place, there are some additional mechanics/rules that will now activate.
Travelling
The Underdark is a dark twisty place. As such, travel is significantly slower than those of you used to overland travel would expect. There are three speeds your party can move at as an adventuring group: Slow, Normal, Fast.
Fast - You move 8 miles per day, but take a -5 penalty to all Perception checks and you cannot forage for sustenance.
Normal - You move 6 miles per day, but suffer no penalties and gain no benefits.
Slow - You move at 4 miles per day, but gain advantage on Survival checks for foraging and Stealth checks.
Marching Order
As the Underdark is full of tunnels and passageways, you will sometimes be in narrow confines where you must move single file, sometimes in standard passages where you can move two abreast, and sometimes in wide open underground caverns where you can move in whatever shifting manner you want.
As such, I ask that you all chatter and come up with two marching orders for me: one single file order, one 2 abreast order.
Lighting
You are underground. Those of you with darkvision can see according to the darkvision description in your race. Typically this is black and white/grey tone only and you can realistically only see something like 60 - 120'. If you have torches or something of that nature, please let me know (so I know for encounter perception and such).
Navigation
Currently, your Navigator is Sarith. Every time you set out from a short or long rest, he will make a Survival check (+5 if moving at a slow pace, -5 if moving at a fast pace). Failed checks will cause you all to wander lost for a few hours until he can recheck. If you would all prefer to nominate a different Navigator, you may. Jimjar, Topsy, Turvy, and Buppido can navigate at a -2 modifier. Sarith can navigate at a 0 modifier. Shuushar can navigate only when you are near to or in the Darklake. All other NPCs navigate at a -10 modifier. I will allow Bildaweer to navigate at a -2 as well (has been in the Underdark, but not nearly with the experience that your drow 'compatriot' has.
Mapping
If you have someone focus only on mapping your progress (they do not make perception checks to notice threats, they don't forage for food, they only focus on documenting your travels) you will end up with a map that will allow you to retrace your steps/navigate an area without needing Survival checks to avoid getting lost.
Foraging
You start off with 4 days of food for everyone. Once that runs out, you will need to forage. If you move at a normal or slow pace, you can forage with a Survival check. Typically this will be against a DC of 15. In some areas (which I'll indicate when you arrive), the DC goes up to 20. Additionally, any magic you may have access to (create food and water, goodberry, etc) can be used to bypass the need to forage for food and water. Additionally, creatures and denizens of the Underdark may have food on them (or may be edible themselves).
Timekeeping
There is no sun, no seasons, no weather, nothing to help you note the time. You can only really judge the time by your rest cycles. However, if you get creative with things, you may be able to come up with a way to tell some semblance of time. :)
Faerzress
Sarith (and the other Underdark people) tell you of a mysterious magical energy called "faerzress" that pervades much of the Underdark. Areas suffused with faerzress can range in size from a few dozen feet across to several miles in diameter and has the following effects for you:
Always dimly lit.
Advantage for all creatures in the area on saving throws against divination spells. If the spell normally doesn't allow a saving throw, the caster must make a Constitution saving throw with a DC of 15 in order to cast the spell. Failing means the spell is wasted.
Teleporting in suffused areas is very difficult. You must make a Constitution saving throw with a DC of 15 in order to succeed. If the check is failed, the creature suffers force damage and the attempt fails. If the check is passed, the spell faces an increased mishap chance.
Spellcasting is a strange thing. Any spell cast must be accompanied by an additional D20 and D100 rolls. On a 1 random number that I will roll each travel day, your 100 roll will be applied to the sorcerer's Wild Magic Surge table.
Nature Checks
For those of you that aren't Underdark races, a Nature check can identify fungi for type and properties. Bildaweer, you will automatically pass this as your race passes this information along.
Pursuit
You are being pursued by the drow from Velkynvelve. Actions you take can increase or decrease your pursuit level (which is a hidden number from you). The higher it is, the more likely the Mistress and minions are to catch you and punish you all. The lower it is, the safer you are from her. I will leave the ways you can decrease your score up to you to discover. Just know that dallying about and extended times fighting creatures will increase your score.
NPCs
Right now, the NPCs are just following along like puppies. After the first few days, once you've all settled into a routine, I will likely have you all pick up one or two of the NPCs to use as a minion. Stool will not be one of these as I want to continue playing him ;). That and it means you will all get 2 NPCs as a resource. I'll give you each a very short stat sheet that details critical things for their action. They will act on your turn in any combat situation and you will get to manage the bulk of their actions. I'll still provide their information and such as I have so far. Hopefully this works out (also keeps me from having to make 9 different sets of checks all the dang time).
How we will handle travel
This experience is not one measured in minutes, or even hours. This is an experience of days and months. As such, to avoid the triviality and boredom of role playing "I walk. I walk. I scratch my butt. I walk." we will be using a different more hand-wavy method.
You will be broken up into roles:
Foragers
Scouts
Navigator
Cartographer
I will roll behind the scenes to determine how many days have elapsed (using a d4) since we last dropped into the scene. The assumption is during the days that elapsed, nothing of interest happened, rote wandering. Each day that we play will have a few phases:
Check Phase - Everyone will make their role's daily checks. Once this is done, I will use the information to breathe some life into the other two phases.
Travelling Phase - A chance to RP some stuff. This is when the bulk of your encounters could happen. We'll handle all those as we get up to them. Additionally, this is where the results of your role checks will manifest. This block will play more like we have been so far.
Making Camp - The end of the travelling day. There is a chance an encounter will happen at this stage. Another RP session, again it will play a little more like we have so far.
Any time your elapsed time would have had you reach a location, I'll let you know where you are and we'll play from there. :)
TL;DR;
The Underdark is a scary place. Many new things and a bunch of checks to make to survive this alien place. Let's do it up.
1st Edit - Changed from a nat 1 to a random number that I roll each travel day for the faerzress effect. I like the added randomness. :)